Question: Simplify the following expression: $\dfrac{66n^5}{22n^5}$ You can assume $n \neq 0$.
$ \dfrac{66n^5}{22n^5} = \dfrac{66}{22} \cdot \dfrac{n^5}{n^5} $ To simplify $\frac{66}{22}$ , find the greatest common factor (GCD) of $66$ and $22$ $66 = 2 \cdot 3 \cdot 11$ $22 = 2 \cdot 11$ $ \mbox{GCD}(66, 22) = 2 \cdot 11 = 22 $ $ \dfrac{66}{22} \cdot \dfrac{n^5}{n^5} = \dfrac{22 \cdot 3}{22 \cdot 1} \cdot \dfrac{n^5}{n^5} $ $\phantom{ \dfrac{66}{22} \cdot \dfrac{5}{5}} = 3 \cdot \dfrac{n^5}{n^5} $ $ \dfrac{n^5}{n^5} = \dfrac{n \cdot n \cdot n \cdot n \cdot n}{n \cdot n \cdot n \cdot n \cdot n} = 1 $ $ 3 \cdot 1 = 3 $